Variable selection for semiparametric varying coefficient partially linear models

Zhao, Peixin; Xue, Liugen

doi:10.1016/j.spl.2009.07.004

Cited by 59 publications

(29 citation statements)

References 17 publications

(38 reference statements)

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“…(ii) For the given sample size n, the performances of the estimators defined by (14) and (15) are similar, but the latter is easy to implement. …”

Section: Numerical Resultsmentioning

confidence: 99%

“…The following theorem gives the convergence rate of the estimators defined by (14) and (15) based on two variable selection procedures.…”

Section: Theorem 1 Suppose That the Regularity Conditions (A1)-(a5) mentioning

confidence: 99%

“…Theorem 2 implies that the estimators defined by (14) and (15) also achieve the optimal convergence rate if the subset of true zero coefficients are already known by choosing the proper tuning parameters. Under some regularity conditions, we show that such consistent estimators must possess the sparsity property, which is stated as follows.…”

Section: Theoremmentioning

confidence: 99%

“…To simplify the computation, we choose the number of interior knots K using the procedure in Zhao and Xue [14]. We first can choose K by minimizing the following cross-validation score.…”

Section: Tuning Parameters Selectionmentioning

confidence: 99%

“…whereβ λ denotes the estimators defined by (14) and (15) given λ. As in Zhou, Alan and Wang [15], we take h = Cn −1/3 , and h l =σ X l h, where σ X l is the estimated standard deviation of X l in the sample.…”

Section: Tuning Parameters Selectionmentioning

confidence: 99%

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Variable Selection for Additive Models with Missing Response at Random

Wu¹,

Zhang²,

Li³

2017

JAS

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This paper studies the problems of variable selection and estimation in the additive models with missing response at random. Based on the centered spline basis function approximation, we propose two new imputed estimating equation methods to implement the variable selection for the additive models with missing response at random by using the smooth-threshold estimating equation. Two new imputed methods can select the significant variables and estimate the unknown functions simultaneously. The proposed methods not only avoid the problem of solving a convex optimization, but also reduce the burden of computation. With the proper choices of the regularization parameter, we show that the resulting estimators enjoy the oracle property. The data driven method is used to choose the tuning parameter. A numerical study is analyzed to confirm the performance of the proposed methods.

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“…(ii) For the given sample size n, the performances of the estimators defined by (14) and (15) are similar, but the latter is easy to implement. …”

Section: Numerical Resultsmentioning

confidence: 99%

“…The following theorem gives the convergence rate of the estimators defined by (14) and (15) based on two variable selection procedures.…”

Section: Theorem 1 Suppose That the Regularity Conditions (A1)-(a5) mentioning

confidence: 99%

Section: Theoremmentioning

confidence: 99%

“…To simplify the computation, we choose the number of interior knots K using the procedure in Zhao and Xue [14]. We first can choose K by minimizing the following cross-validation score.…”

Section: Tuning Parameters Selectionmentioning

confidence: 99%

Section: Tuning Parameters Selectionmentioning

confidence: 99%

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